CN106936407B - Frequency domain block least mean square adaptive filtering method - Google Patents
Frequency domain block least mean square adaptive filtering method Download PDFInfo
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Abstract
The invention provides a frequency domain block least mean square self-adaptive filtering method, aiming at providing a self-adaptive filtering method which can balance a non-minimum phase system, has the same convergence with a time domain LMS algorithm and has lower calculation complexity, and the invention is realized by the following technical scheme: firstly, a data sequence to be filtered is converted into parallel data blocks with the length of L in a serial-parallel mode, M/2 data are respectively cascaded from the adjacent front parallel data blocks and the adjacent rear parallel data blocks to form cascaded data blocks with the length of N being L + M, Fast Fourier Transform (FFT) operation is carried out on the cascaded data blocks to obtain N frequency domain input data, then the N frequency domain input data are multiplied by N filter weight coefficients to obtain frequency domain data filtered by N filters, and N-point Fourier inverse transform (IFFT) is carried out on the frequency domain data to obtain N filtered time domain data. Multiplying the N frequency domain error signals by the conjugates of the N frequency domain input data, and carrying out IFFT transformation to obtain a time domain gradient vector with the length of N; and updating the weight coefficient of the self-adaptive filter to obtain a processed frequency domain gradient vector.
Description
Technical Field
The invention relates to a frequency domain block least mean square (FBLMS) adaptive filtering algorithm in the field of adaptive signal processing.
Background
Adaptive signal processing is an important branch of the signal processing field. Through decades of development, the adaptive filtering theory, which is the basis of adaptive signal processing, has been widely applied to communication systems, control systems, and other various systems. In a communication system, a received signal may be interfered by various noises, which affects the transmission quality of the signal, and therefore, it is necessary to design a filter for interference cancellation to filter the signal. In practical application, because the characteristics of the interference signal are not easy to know, most of the interference is time-varying or even non-stationary, so that the purpose of filtering the interference cannot be achieved by a conventional filter, and the self-adaptive filter can track the characteristics of the interference signal, automatically adjust the performance of the self-adaptive filter and better eliminate the interference. For an adaptive interference cancellation system, an original signal containing unknown interference is used as a reference signal of an adaptive filter, and an interference signal emitted by the same interference source is used as an input signal. The weight coefficient of the self-adaptive filter is adjusted to enable the output of the filter to tend to interference signals, and then the interference is eliminated through the phase reducer. The implementation of adaptive filtering in the frequency domain is to perform adaptive adjustment of filter parameters in the frequency domain. The adaptive process generally adopts a typical LMS adaptive algorithm, but when the input signal of the filter is a colored random process, especially when the input signal is highly correlated, the convergence speed of the algorithm is reduced greatly, mainly because the convergence performance of the algorithm is deteriorated and the steady-state error is increased due to the increased dispersion degree of the characteristic values of the autocorrelation matrix of the input signal. In this case, if the transform domain algorithm is adopted, the convergence speed of the algorithm can be increased. The basic idea of the transform domain algorithm is: the input signal is first orthogonally transformed to remove or attenuate its correlation and then the transformed signal is applied to an adaptive filter to perform a filtering process to improve the condition number of the correlation matrix. The frequency domain block LMS and FBLMS algorithms are widely applied because the DFT has approximate orthogonality and is added with the FFT fast algorithm. The FBLMS algorithm essentially implements the time-domain block LMS algorithm in the frequency domain, i.e., time-domain data is grouped into data blocks of N points, and the filter weight coefficients remain unchanged at each block. The FBLMS algorithm can be implemented in the frequency domain by an overlap-and-hold method in digital signal processing, which is significantly less computationally intensive than the time domain method, or by an overlap-and-add method, but this algorithm requires a larger amount of computation than the overlap-and-hold method. The fast fourier transform FFT reduces the amount of computation by frequency domain multiplication instead of time domain convolution. The frequency domain adaptive algorithm is based on Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT), and aims to perform an adaptive filtering algorithm with respect to its characteristics by transforming an input signal into a frequency domain.
In 1959, Widrow and Hoff et al proposed a famous time domain LMS (Least Mean Square) adaptive filtering algorithm when studying a pattern recognition scheme of adaptive linear elements. The time domain LMS adaptive filtering algorithm determines the coefficient based on gradient optimization, and has the advantages of simple realization structure, small calculation amount, good stability and the like. Therefore, among various adaptive filtering algorithms, the LMS algorithm is widely used because it is simple, small in calculation amount, good in stability, and easy to implement. However, the time-domain LMS adaptive filtering algorithm has some drawbacks, which may result in a significant increase in complexity of the algorithm when the number of filtering taps is large. The frequency domain block LMS algorithm can be effectively applied to the self-adaptive filtering of the number of the long tap coefficients, particularly for signals with sparse characteristics, the operation amount can be obviously reduced, and the complexity is reduced. The LMS algorithm of frequency domain block is to adjust the filter coefficient block by block, and its core lies in calculating the linear convolution of the filter tap coefficient and the input signalAnd a linear correlation of the input signal and the error signal. If the length is N2The length of the sequence x (n), h (n) is very different, for example, h (n) is a unit impulse response of a certain filter, the length is limited, and the sequence is used for processing a very long input signal x (n), or a continuous signal is processed, according to the method, h (n) needs to be compensated with a plurality of zeros for calculation, and the calculation amount is very waste or cannot be realized at all. In order to maintain the superiority of the fast convolution method, x (n) can be divided into a plurality of sections for post-processing, the length of each section is close to h (n), and the processing methods are two types: overlap add and overlap save. According to the theory of digital signal processing, the FFT technique provides a powerful tool for fast convolution and fast correlation, and two methods, namely, the overlap-and-hold method and the overlap-and-add method, can be adopted, wherein the overlap-and-hold method is more commonly used. The core of the block LMS algorithm is to compute the linear convolution of the filter tap coefficients and the input signal and the linear correlation of the input signal and the error signal. When the FFT algorithm is used to calculate the fast convolution, overlap-and-hold method can be used, and when 1/2 overlap is performed, the block size is equal to the number of coefficients, where the operation efficiency is the highest. That is, M zeros are compensated after the tap coefficients of the M-point filter, and then N-point FFT is performed, where N is 2M.
The existing frequency domain block LMS adaptive filtering algorithm adopts an overlap-preserving method in calculating fast convolution, namely M zeros are compensated after M point filter tap coefficients, and then 2M point FFT is carried out. The method is only suitable for the minimum phase system, and the non-minimum phase system cannot be balanced. And when all the zero points of the linear time-invariant system are positioned in the unit circle, the system is the minimum phase system, and otherwise, the system is the non-minimum phase system.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a frequency domain block least mean square adaptive filtering method which can ensure the convergence same as that of a time domain LMS algorithm, has lower calculation complexity and can achieve the capability of balancing a non-minimum phase system by improving the conventional FBLMS algorithm so as to solve the problem that the conventional FBLMS algorithm cannot balance the non-minimum phase system.
The above object of the present invention can be achieved by the following means. A frequency domain block least mean square adaptive filtering method is characterized by comprising the following steps:
firstly, an input data sequence to be filtered is converted into parallel data blocks with the length of L in a serial-parallel mode, M/2 data are respectively cascaded from the adjacent front parallel data blocks and the adjacent rear parallel data blocks to form cascaded input data blocks with the length of N being L + M, Fast Fourier Transform (FFT) operation is carried out on the cascaded input data blocks to obtain N frequency domain input data, then the N frequency domain input data are multiplied by N filter weight coefficients one by one, then N point Fourier inverse transform (IFFT) is carried out on the frequency domain data filtered by the N filters to obtain N filtered frequency domain data, N frequency domain error signals are multiplied by the conjugation of the N frequency domain input data one by one, and IFFT transform is carried out to obtain a time domain gradient vector with the length of N; and calculating linear convolution sum and linear correlation by using the cyclic convolution of the sequence, wherein the current filter weight coefficient is the weight of the filter at the last moment and the product of the frequency domain gradient vector and the iteration step length, and the current filter weight coefficient is used as an updated filter weight coefficient to obtain a processed frequency domain gradient vector.
Compared with the prior art, the invention has the beneficial effects that:
1. the convergence equal to that of the time domain LMS algorithm can be ensured. The method comprises the steps of converting an input data sequence to be filtered into parallel data blocks with the length of L in a serial-parallel mode, respectively cascading M/2 data from adjacent front and back parallel data blocks to form a cascading input data block with the length of N being L + M, performing Fast Fourier Transform (FFT) operation on the cascading input data block to obtain N frequency domain input data, multiplying the N frequency domain input data by N filter weight coefficients one by one, performing inverse Fourier transform (IFFT) on N points of the frequency domain data filtered by the N filters to obtain N filtered frequency domain data, discarding M/2 data at two ends of time domain data, and reserving and storing data with the length of N middle filtered time domain data; when calculating the fast convolution, the overlap-preserving method adopted by the prior art is changed into the method that M/2 zeros are respectively compensated before and after the tap coefficient of the L-point filter, and then the FFT is carried out at L + M points, wherein 1/2 overlap is carried out when L is equal to M, and the operation efficiency is highest. A frequency domain block least mean square adaptive filtering method with the capability of equalizing non-minimum phase systems is provided.
2. There is less computational complexity. Multiplying N frequency domain error signals with the conjugation of N frequency domain input data one by one, performing IFFT to transform to a time domain to obtain a length E (k) as a time domain gradient vector of N, calculating linear convolution and linear correlation by using cyclic convolution of a sequence, setting M time domain gradient data in the middle to be 0, reserving L data at two ends, and obtaining the frequency domain gradient vector of the length N from IFFT to the frequency domain through inverse Fourier transform; and then deleting partial data, filling 0, and updating the weight coefficient of the adaptive filter by taking the weight coefficient of the current filter as the weight coefficient of the updated filter, which is the sum of the weight of the filter at the last moment and the product of the frequency domain gradient vector and the iteration step length, so as to obtain the processed frequency domain gradient vector. The frequency domain block LMS algorithm not only ensures the convergence same as the time domain LMS algorithm, but also utilizes the rapid FFT technology to calculate the linear convolution and the linear correlation by the cyclic convolution of the sequence, thereby greatly reducing the operation amount. Meanwhile, the algorithm can not cause error accumulation, the real-time performance of the algorithm is better when the algorithm is realized with effective precision, and the continuous work of the filter can be ensured.
3. The ability to equalize non-minimum phase systems can be achieved. The invention improves the prior FBLMS algorithm, changes the zero filling mode of the filter tap, and can achieve the capability of balancing the non-minimum phase system. Specifically reflecting the implementation structural changes to the following modules: the method comprises an input data block cascade mode, a filtering result effective data output mode, an error signal 0 complementing mode and a gradient constraint mode. On the basis of not increasing the implementation complexity, the problem that the existing FBLMS algorithm cannot balance the non-minimum phase system is effectively solved.
The invention is equally applicable to minimum phase systems.
Drawings
Fig. 1 is a block diagram of an implementation of the frequency domain block least mean square adaptive filtering method of the present invention.
The invention is further illustrated with reference to the figures and examples.
Detailed Description
See fig. 1. According to the method, firstly, an input data sequence to be filtered is converted into parallel data blocks with the length of L in a serial-parallel mode, M/2 data which are respectively cascaded from adjacent front and back parallel data blocks form a cascaded input data block with the length of N being L + M, Fast Fourier Transform (FFT) operation is carried out on the cascaded input data block to obtain N frequency domain input data, then the N frequency domain input data are multiplied by N filter weight coefficients one by one, N points are carried out on the frequency domain data filtered by the N filters to carry out IFFT to obtain N filtered frequency domain data, M/2 data at two ends of time domain data are abandoned, and N data which are centered in the filtered time domain data are reserved and stored; for the retained centered data, performing equal-interval extraction by using a ratio R of a tap rate of an equalizer and a signal rate, outputting a 1 st number, a 1+ R number, a 1+2R number and … … to obtain L/R effective output data y (N), subtracting the effective output data y (N) from expected data e (N) to obtain L/R error signals, performing interpolation by using R as a factor, namely inserting R-1 0 at each time interval R at two ends of each error signal e (N) to obtain an error data block with the length of L, filling M/2 0 at two ends of the error data block respectively, namely supplementing M/2 zeros before and after a tap coefficient of a filter, and performing N-point FFT on the obtained error data block with the length of N-L + M to obtain N frequency domain error signals; multiplying N frequency domain error signals by the conjugation of N frequency domain input data one by one, performing IFFT to transform to a time domain to obtain a length E (k) as a time domain gradient vector of N, calculating linear convolution and linear correlation by using cyclic convolution of a sequence, setting M time domain gradient data in the middle to be 0, reserving L data at two ends, and obtaining the frequency domain gradient vector of the length N from IFFT to the frequency domain through inverse Fourier transform; and then deleting partial data, filling 0, and updating the weight coefficient of the adaptive filter by taking the weight coefficient of the current filter as the weight coefficient of the updated filter, which is the sum of the weight of the filter at the last moment and the product of the frequency domain gradient vector and the iteration step length, so as to obtain the processed frequency domain gradient vector.
When R is 1, the equalizer is an integer interval equalizer; when R >1, it is a fractionally spaced equalizer. 1/2 overlap when L-M,
comprises the following steps:
1) and performing serial-parallel conversion on the input data sequence to be filtered to obtain a parallel data block with the length of L, and respectively cascading M/2 data with the adjacent front and rear parallel data blocks to obtain a cascaded input data block with the length of N being L + M.
2) And (2) performing FFT (fast Fourier transform) on the cascaded input data block with the length of N obtained in the step (1) to obtain N frequency domain input data.
3) And (3) multiplying the N frequency domain input data obtained in the step (2) by the N filter weight coefficients one by one to obtain N filtered frequency domain data. Wherein, the N filter weight coefficients are obtained by the following steps (5), (6) and (7).
4) And (4) performing N-point IFFT on the filtered frequency domain data obtained in the step (3) to obtain N filtered time domain data, reserving the central L data, and discarding M data at two ends. For the reserved L data, performing extraction by a factor R to obtain L/R effective output data, wherein R is the ratio of the tap rate of the equalizer to the signal rate, and when R is 1, the R is an integer interval equalizer; when R >1, it is a fractionally spaced equalizer.
5) And (4) subtracting the expected data from the effective output data in the step (4) to obtain L/R error signals. And interpolation is carried out by a factor R, namely R-1 0 is inserted behind each error signal to obtain a data block with the length of L, then M/2 0 is respectively filled at the two ends of the data block to obtain a data block with the length of N being L + M, and finally N-point FFT conversion is carried out to obtain N frequency domain error signals. Where the desired data results from a decision to validly output data, a training sequence may also be employed.
6) Gradient vector processing: and (3) multiplying the N frequency domain error signals obtained in the step (5) by the conjugates of the N frequency domain input data obtained in the step (2) one by one, performing IFFT to transform to a time domain to obtain time domain gradient vectors with the length of N, setting M time domain gradient data in the middle to be 0, reserving L data at two ends, and finally transforming to the frequency domain through FFT to obtain the frequency domain gradient vectors with the length of N.
7) And updating the weight coefficient of the filter. The current filter weight coefficient is the filter weight at the last moment plus the product of the frequency domain gradient vector and the iteration step.
Suppose the input signal to be filtered is x (n), after serial-to-parallel conversion, it is falseLet the kth data block be [ x (kL), …, x (kL + L-1)]TLength is L, and M/2 data are respectively cascaded with adjacent front and back parallel data blocks to obtain a k-th filtered cascade input data block x (k):
wherein, x represents the cascade input data block with the length of N ═ L + M, x (k) represents the cascade input data block of the k-th filtering, k is a natural number, and the superscript T represents the transposition of the vector or the matrix. The input data is FFT transformed to the frequency domain to obtain the frequency domain input data X (k) with the length of N:
X(k)＝diag{Fx(k)} (2)
wherein diag { } represents converting the vector into a diagonal matrix, and the matrix F is a Fourier transform matrix
Let the filter frequency domain tap coefficient of the kth filtering be W (k), where W (k) is a column vector of Nx 1. The filter frequency domain output is an Nx 1-dimensional vector
Y(k)＝X(k)W(k) (3)
Is transformed into the time domain
y1(k)＝F-1Y(k) (4)
Then the nx 1 dimensional time domain vector y1(k) Is composed of
y1(k)＝[y1(k,1),y1(k,2),…,y1(k,N)]T
By adopting an overlap-save method, invalid data at two ends are removed, namely effective filtering data is
y2(k)＝[y1(k,M/2+1),y1(k,M/2+2),…,y1(k,L+M/2)]T (5)
Then the lx 1-dimensional time domain vector y2(k) Is composed of
y2(k)＝[y2(k,1),y2(k,2),…,y2(k,L)]T
Finally, taking R as an interval pair y2(k) Decimating to obtain a final filtered output of
y(k)＝[y2(k,1),y2(k,1+R),y2(k,1+2R),…]T (6)
Where R is the ratio of the equalizer tap rate to the signal rate. When R is 1, the equalizer is an integer interval equalizer; when R >1, it is a fractionally spaced equalizer.
In calculating the filter frequency domain tap coefficients W (k), an error signal is first calculated from the output signal y (k), i.e.
e(k)＝d(k)-y(k) (7)
Where d (k) is the desired data vector, which can be obtained from y (k) hard decisions. Denote (L/R) × 1-dimensional time domain vector e (k) as
e(k)＝[e(k,1),e(k,2),…,e(k,L/R)]T
Next, the (L/R) × 1-dimensional time domain error signal is transformed into an N × 1-dimensional frequency domain error signal by inserting 0, and the following steps are required: firstly, inserting R-1 0 s into each number of error signals e (k) to obtain a vector with length of L, then respectively filling M/2 0 s into two ends of the vector to obtain a vector with length of N, and finally performing N-point FFT (fast Fourier transform) to obtain a frequency domain error signal vector, namely
Since the computation of the time-domain gradient vector in the block LMS algorithm is a linear correlation of the input signal and the error signal, a fast correlation operation can be performed using FFT. Therefore, after the input signal and the error signal are transformed to the frequency domain, the input signal and the error signal are directly multiplied, and then gradient constraint is carried out, so that the result is consistent with the time domain algorithm result. The time-domain gradient vector is calculated as
The gradient constraint is then applied. Dividing the Nx 1-dimensional time-domain gradient vector
Is marked as
And setting the number of the middle M as 0, the constrained frequency domain gradient vector is
And finally, updating the weight coefficient of the filter for filtering for the (k +1) th time:
W(k+1)＝W(k)+μΦ(k) (11)
where μ is the iteration step.
Claims (10)
1. A frequency domain block least mean square adaptive filtering method is characterized by comprising the following steps: firstly, converting an input data sequence string to be filtered into a parallel data block with the length of L, respectively cascading M/2 data from the front and the back of the parallel data block to form a cascading input data block with the length of N-L + M, performing Fast Fourier Transform (FFT) operation on the obtained cascading input data block with the length of N to obtain N frequency domain input data, performing serial-parallel conversion on an input signal x (N) to obtain a parallel data block with the length of L, respectively cascading M/2 data from the front and the back of the parallel data block, and then performing FFT conversion to obtain a cascading input data block X (k) of the kth filtering; calculating an error signal according to an output signal y (k), utilizing a filter frequency domain tap coefficient W (k) of the kth filtering to obtain a filter frequency domain output Nx 1-dimensional vector Y (k), multiplying an input data block X (k) with the Nx 1-dimensional vector Y (k), simultaneously carrying out gradient vector processing, multiplying the obtained N frequency domain input data with N filter weight coefficients one by one, carrying out N-point Fourier inverse transform (IFFT) on the frequency domain data filtered by the N filters to obtain N filtered frequency domain data and a time domain gradient vector with the length of N, and discarding M/2 data at two ends of the time domain data; at the ratio of equalizer tap rate to signal rateExtracting R as a factor to obtain L/R effective output data y (n); subtracting the obtained L/R effective output data y (N) from the expected data d (N), subtracting to obtain L/R error signals, compensating 0 for the input error signals e (N), inserting R0 s into the error signals e (N) every R effective output data to obtain error signals e (N) with the length of L, filling M/2 0 s into the two ends of the error signals respectively to obtain vectors with the length of N, and finally performing N-point FFT (fast Fourier transform) to obtain a k-th frequency domain error signal vector E (k); the input signal X (n) is transformed to the frequency domain through Fast Fourier Transform (FFT), and then the cascade input data block X (k) is obtained, and the output data X can be obtained after the conjugation of the X (k)H(k) Then, the data X is outputtedH(k) Multiplying the k-th time frequency domain error signal vector E (k), and obtaining a time domain gradient vector with the length of N by IFFT to the time domain through inverse Fourier transform
Calculating linear convolution and linear correlation by using cyclic convolution of the sequence, setting the M central time domain gradient data as 0 after the linear correlation, and reserving data at two ends; then, making gradient constraint, updating the weight coefficient of the filter, and taking the current weight coefficient of the filter as the weight of the filter at the last moment and the product of the frequency domain gradient vector and the iteration step as the weight coefficient of the updated filter to obtain the updated frequency domain gradient vector, wherein L, M, N is a natural number.
2. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein in calculating the fast convolution, M/2 zeros are supplemented before and after the tap coefficients of the L-point filter, and then L + M-point FFT is performed, wherein 1/2 overlap occurs when L is M.
3. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein for the retained centered data, the 1 st number, the 1+ R number, the 1+2R number, and … … are outputted by performing equal-interval extraction with the ratio R of the equalizer tap rate to the signal rate to obtain L/R effective output data y (n), and L/R error signals are obtained by subtracting the effective output data y (n) from the expected data d (n), where R is the ratio of the equalizer tap rate to the signal rate and n is a natural number.
4. The frequency-domain block least mean square adaptive filtering method of claim 3, wherein when R is 1, it is an integer interval equalizer; when R >1, it is a fractionally spaced equalizer.
5. The frequency-domain block least mean square adaptive filtering method of claim 3, wherein the desired data is generated from a decision result of the valid output data or L/R valid output data of the training sequence is employed.
6. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein, in order to distinguish signals at different time instants, the input signal to be filtered is denoted as x, x (n) denotes the input signal at the nth time instant, and after serial-to-parallel conversion, the kth data block is [ x (kL), …, x (kL + L-1)]TThe length is L, M/2 data are respectively cascaded from the front and the back of the parallel data block to obtain a k-th filtering cascade input data block
Where k is a natural number, the superscript T represents the transpose of the vector or matrix, and n is a natural number.
7. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein the vector is converted into a diagonal matrix diag { }, and FFT-transformed into the frequency domain using the input data to obtain a frequency-domain input data block x (k) of length N and a fourier transform matrix F, and the k-th filtered length frequency-domain input data block x (k) ═ diag { fx (k) }
And a Fourier transform matrix F, denoted as
Wherein e is a natural logarithm, π is a circumferential ratio, j is an imaginary number, j2＝-1。
8. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein the filter frequency domain output nx1-dimensional vector is y (k) ═ x (k) w (k), and is transformed to the time domain into y (k) — y1(k)＝F-1Y (k), then Nx 1 dimensional time domain vector y1(k) Is y1(k)＝[y1(k,1),y1(k,2),…,y1(k,N)]TThe overlap reservation method is adopted to remove invalid data at two ends, namely the valid filtering data is y2(k)＝[y1(k,M/2+1),y1(k,M/2+2),…,y1(k,L+M/2)]TThen L x 1 dimensional time domain vector y2(k) Is y2(k)＝[y2(k,1),y2(k,2),…,y2(k,L)]TAnd finally, taking R as an interval to pair y2(k) The final filter output is obtained by decimation as y (k) ═ y2(k,1),y2(k,1+R),y2(k,1+2R),…]T
Where w (k) is the filter frequency domain tap coefficient for the kth filtering, and R is the ratio of the equalizer tap rate to the signal rate.
9. The frequency-domain block least mean square adaptive filtering method of claim 1, wherein in the process of calculating the frequency-domain tap coefficients w (k), the k-th filtered output signal y (k) is obtained by hard decision, the output signal y (k) is subtracted from the k-th filtered expected data vector d (k), the k-th filtered error signal e (k) ═ d (k) -y (k) is obtained, and the (L/R) × 1-dimensional time-domain vector e (k) is recorded as e (k) ═ e (k,1), e (k,2), …, e (k, L/R)]TNext, the (L/R) × 1-dimensional time domain error signal is transformed into an N × 1-dimensional frequency domain error signal by inserting 0, and the following processing is performed: inserting R-1 0 after each number of error signals e (k) to obtain a vector with length L, and filling M/2 0 at two ends of the vector to obtain a vector with length NFinally, performing N-point FFT to obtain frequency domain error signal vector,
10. the frequency-domain block least mean square adaptive filtering method of claim 1, wherein the adaptive filtering is based on time-domain gradient vectors
Inverse F of the Fourier transform F-1Frequency domain error signal vector E, frequency domain error signal vector E (k) of k-th filtering, H represents the conjugate of vector or matrix, and time domain gradient vector of k-th filtering is calculated
Then making gradient constraint; dividing the Nx 1-dimensional time-domain gradient vector
Is marked as
The constrained k-th filtered frequency domain gradient vector is
And finally, updating the weight coefficient W (k +1) of the filter for filtering for the (k +1) th time: w (k +1) ═ W (k) + μ Φ (k)
Wherein the content of the first and second substances,
representing an element in a temporal gradient vector,
time-domain gradient vectors calculated for the k-th filtering respectivelyAnd setting the middle M number as 0, W represents the filter weight coefficient, W (k) is the filter weight coefficient of the kth filtering, W (k +1) is the filter weight coefficient of the kth filtering, mu is the iteration step size, and phi (k) is the frequency domain gradient vector of the kth filtering.
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| CN110413944A (en) * | 2018-04-28 | 2019-11-05 | 中国科学院沈阳自动化研究所 | A kind of information extracting method based on convolution sequence transformation |
| CN108919227B (en) * | 2018-08-17 | 2021-12-31 | 电子科技大学 | Multichannel FBLMS implementation method based on GPU acceleration |
| CN109102821B (en) * | 2018-09-10 | 2021-05-25 | 思必驰科技股份有限公司 | Time delay estimation method, time delay estimation system, storage medium and electronic equipment |
| CN108918929B (en) * | 2018-09-11 | 2020-12-04 | 广东石油化工学院 | Power signal self-adaptive filtering method in load decomposition |
| CN110492869B (en) * | 2019-08-06 | 2023-06-06 | 南京大学 | Improved segmentation frequency domain block LMS self-adaptive filtering algorithm |
| CN111131099B (en) * | 2019-12-05 | 2022-05-31 | 北京航空航天大学杭州创新研究院 | Same-frequency full-duplex-oriented low-complexity FBLMS self-interference cancellation implementation method |
| CN111506294B (en) * | 2020-04-13 | 2022-07-29 | 中国科学院自动化研究所 | FPGA (field programmable Gate array) implementation device and method based on FBLMS (fiber bulk mean Square) algorithm of block floating point |
| CN112787632B (en) * | 2020-12-22 | 2022-11-08 | 上海航天控制技术研究所 | Low-calculation-quantity real-time adaptive filtering method for steering engine |
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